Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics

Abstract

We have developed a Kramers-Kronig consistent analytical expression to fit the measured optical functions of hydrogenated amorphous silicon (a-Si:H) based alloys, i.e., the real and imaginary parts of the dielectric function (⑀ 1 ,⑀ 2) ͑or the index of refraction n and absorption coefficient ␣͒ versus photon energy E for the alloys. The alloys of interest include amorphous silicon-germanium (a-Si 1Ϫx Ge x :H) and silicon-carbon (a-Si 1Ϫx C x :H), with band gaps ranging continuously from ϳ1.30 to 1.95 eV. The analytical expression incorporates the minimum number of physically meaningful, E independent parameters required to fit (⑀ 1 ,⑀ 2) versus E. The fit is performed simultaneously throughout the following three regions: ͑i͒ the below-band gap ͑or Urbach tail͒ region where ␣ increases exponentially with E, ͑ii͒ the near-band gap region where transitions are assumed to occur between parabolic bands with constant dipole matrix element, and ͑iii͒ the above-band gap region where (⑀ 1 ,⑀ 2) can be simulated assuming a single Lorentz oscillator. The expression developed here provides an improved description of ⑀ 2 ͑or ␣͒ in the below-band gap and near-band gap regions compared with previous approaches. Although the expression is more complicated analytically, it has numerous applications in the analysis and simulation of thin film a-Si:H based p-in and n-i-p multilayer photovoltaic devices. First, we describe an approach whereby, from a single accessible measure of the optical band gap, the optical functions can be generated over the full solar spectrum for a sample set consisting of the highest quality intrinsic a-Si:H based alloys prepared by plasma-enhanced chemical vapor deposition using the principle of maximal H 2 dilution. Second, we describe quantitatively how such an approach can be modified for sample sets consisting of lower quality alloy materials. Finally, we demonstrate how the generated optical functions can be used in simulations of the absorption, reflection, and quantum efficiency spectra of a-Si:H based single-junction and multijunction solar cells.

Spectroscopic ellipsometry characterization of electrochromic tungsten oxide and nickel oxide thin films made by sputter deposition

“…The use of a Lorentz oscillator to represent optical absorption reminiscent of an Urbach tail is not the only possibility, but the logarithmic nature of the band tail can be accounted for explicitly, as done in the past for optical data of amorphous semiconductors [45] and EC films [46]. We believe that the Lorentz oscillator representation is sufficient for our purposes and, furthermore, it can be implemented using standard software [41].…”

Structural and optical properties of visible active photocatalytic WO3 thin films prepared by reactive dc magnetron sputtering

“…7. This marks the demarcation energy, which may be used to approximate the transition between the Urbach tail, 59 and the absorption due to electronic interband transitions. The demarcation energies deduced from the analysis are shown in Table II.…”

Improving solar cell efficiency with optically optimised TCO layers

“…In this way the thickness and dielectric parameters are chosen in a way that the maximum of the broad Fabry-Perot oscillation due to the thin additional layer coincides with the maximum in the quantum efficiency of the cell. A significant increase in transmission can [28] and [29]), absorber (a-Si:H: amorphous silicon, taken from [30]), and a rough interface layer (a-Si:H/SnO 2 :F EMA: Bruggeman EMA 50% a-Si:H in FTO). b) shows the calculated transmission into the absorber for various interface matching materials in comparison to the reference stack without them.…”

“…Figure 5 shows the calculated increase in transmission for stacks consisting of glass/SnO 2 :F/a-Si:H as a reference and such using AlZnO x , MgAl 2 O 4 , and the ideal GT-TCO at the glass/SnO 2 :F interfae. Measured dielectric functions have been used for SnO 2 :F and AlZnO x , while database dielectric functions have been used for MgAl 2 O 4 and a-Si:H [30,41].…”